Compatibility

Some versions of jQuery may not run inside the Greasemonkey sandbox. But, as of this writing, all released versions, from 1.3.2 onward, work with no known issues except the potential conflict discussed below. (The current jQuery version is 1.9.1.)

Potential conflict

In some cases, @required jQuery can conflict with the web page.
In that case, you can use jQuery in noConflict mode at the top of your script:

this.$ = this.jQuery = jQuery.noConflict(true);

It's also possible to force execution in the legacy sandbox, thus isolating your script further from the content page.
Specify specify any @grant value other than none to do this.
See @grant Scope for more information.

jQuery Tools

YUI

Sometimes using the @resource imperative alongside @require can be helpful.

YUI has a nice tool to bundle your required libraries on the fly.
After you receive your script source (Loading Script and CSS Directly box) use the @require key for the script and @resource for the CSS (if any).